Posted
by
samzenpus
on Sunday November 25, 2012 @04:30PM
from the order-is-as-order-does dept.

SternisheFan writes "The structure of the universe and the laws that govern its growth may be more similar than previously thought to the structure and growth of the human brain and other complex networks, such as the Internet or a social network of trust relationships between people, according to a new study. 'By no means do we claim that the universe is a global brain or a computer,' said Dmitri Krioukov, co-author of the paper, published by the Cooperative Association for Internet Data Analysis (CAIDA), based at the San Diego Supercomputer Center (SDSC) at the University of California, San Diego.'But the discovered equivalence between the growth of the universe and complex networks strongly suggests that unexpectedly similar laws govern the dynamics of these very different complex systems,' Krioukov noted."

I have learned after studying many differing fields of science and engineering, that as you master one field you gain insight into many others. There are certain patterns of organization that repeat throughout nature, and mimicked by man, and if you study anything long enough you are certain to see these patterns. The more you learn, the easier it becomes to learn more because natural things are mostly variations on a finite set of themes that, whether you are aware of them or not, you will discover them and from that point forward, notice them much more quickly.

Those repeating patterns are signs of the same math in the background. Sadly, with most mathemathicians doing more abstract work the aren't many who study them. Theoreticists try to fill the void left by the mathematicians and they do a goo job but most of them can't really think outside of their own field.

It's not math. Math is a language. Don't confuse natural phenomena with math; It is possible to observe and even describe them without knowledge of mathematics. That said, math is one of the best ways to describe them.

"In astrophysics and cosmology, the anthropic principle is the philosophical consideration that observations of the physical Universe must be compatible with the conscious life that observes it. Some proponents of the anthropic principle reason that it explains why the Universe has the age and the fundamental physical constants necessary to accommodate conscious life. As a result, they believe it is unremarkable that the universe's fundamental constants happen to fall w

...which, when you think about it, doesn't mean there isn't a conscious force at work trying to brute-force a recipe for life, it just means we don't know either way. Personally, I like the image of a deity who is analogous to a frustrated graduate student trying to grow a crystal for X-ray diffraction.

What's funny is that the anthropic principle by definition doesn't have much meaning. You can restate it as "the universe is the way we see it, because we are seeing it be that way."

The weak anthropic principle always boils down to simple tautology, while the strong anthropic principle flys in the face of biology and works out to puddle thinking. The universe isn't tuned for us, we tuned ourselves for living in the universe through evolution.

Precisely. The universe doesn't change to accommodate us even slightly. Pockets of air will never spring up in the vacuum for our benefit. We are the ones who change in order to fit in the universe and scratch out our existence. The universe doesn't change to make us comfortable.

John Archibald Wheeler was also a supporter of a participatory universe - as noted in the wiki page. Quantum physics needs an observer so the universe evolves to have an observer present to make it happen. So next time you look through a powerful telescope at something no one has seen before, remember, Thou art God

Clearly the structure of the universe dictates the structure of the human brain, but to what extent does the human brain dictate the structure of the universe?

One of our brain's functions is to model the world we live in, but it's not a perfect model. Some information is imperfect or missing. Since the missing information could be tweaked without us ever noticing, does that missing information really exist?

Could it be that we create narratives within only the limited band of which we can perceive and of which we are conscious?

If we do not know our instrument - and only true fools assert that they have mastered an understanding of their mind - then how can we make any ontological assessment of reality? Other than merely provisional and temporally practical, local observations, of course!

I would argue that every non-mathematical correct description of nature is transformable into math by involving the Church-Turing lambda-reductibility thesis.
Axiom 1: A description is made using a language.
Axiom 2: A description is not infinitely long.
A correct non-mathematical description of a natural process using a language. Since that natural process is express as with a language, it is possible to build an interpreter for that a finite set of that language. Since an interpreter is realized-by and realized computations, according to the Church-Turing thesis an equivalent lambda calculus problem exists. Therefore, if the Church-Turing lambda-reductibility thesis hold true, every language based description must have at least one equivalent mathematical problems. I concede that this description is probably useless and really hard to build but it exist nonetheless.

...every language based description must have at least one equivalent mathematical problems.

Well, you're not wrong.:) All languages evolve in complexity to explain the environment of its users. That's just human nature. And being able to count beyond potato is likewise a valuable survival skill, which is how mathematical understanding evolved. I guess I should be more specific in that you don't have to study mathematics specifically in order to observe and report on these natural patterns of organization. It is possible to sketch out these things visually and say "This is like that", without eve

To my mind this belies a misunderstanding of what mathematics is.
It does not depend on any one representation, or encoding. It encompasses any (non-ambiguous) expression of rules and relationships between things (be they real, ideals based on reality, or entirely fictional mental entities), or non-ambiguous measurements, and more importantly, the process of generating, manipulating, and understanding said relationships.
I agree wholeheartedly that our current encoding/names/expressions/forms/system of cate

Math does not tolerate concepts like "A lot", "a little", "somewhat", "sortof", "usually", "often", etc. These are phrases used in everyday conversation to describe not just quantity, but also quality -- but subjectively instead of objectively. And math is not good at subjectivity. Mathematics is discrete -- it has a definite and unambiguous result (whether it is a scalar or vector, a range or a set, whether positive or negative, real, or imagined...). 2x+y may not be solvable without knowing the values of

Recognising, identifying and using patterns is mathematics. By collecting things which demonstrate the fibbonaci sequence together your Kenyan kid is doing mathematics even if he is not very good at formally structuring his thoughts using the conventions form academia.
Ambiguous communication (ie. communcation can mean more than one of the available things that aren't degenerate in the current circumstances) is merely bad communication.
Approximations, qualitative analysis and context dependant communicatio

Pattern recognition does not require an explicit understanding of mathematics.

But ask the question "what is a pattern?" That cannot be answered non-mathematically without ambiguity. Go on, try it. Therefore, the very notion of "pattern" is essentially mathematical. You don't know what mathematics is.

Then show me a strictly non-mathematical, testable model of any real system that provides novel insight into the workings of that system and that has predictive power. Doesn't exist.

That is not to confuse all of perceived reality with a single mathematical model. There is no single mathematical model of reality (a GUT) that does not fail at some point as yet. But we're not talking about reality, we're talking about modeling reality as closely as we can get, an enterprise which is called physics.

I suppose my post was somewhat poorly worded.
To expand/try again somewhat, uhm

First a few things that aren't maths, or that maths is not.
For one, it does not generate entirely new axioms/rules. The results often seem novel, but they are directly implied by the axioms -- a small set of things simply taken to be obvious New mathematics comes from greater insight into previous assumptions, elimination of redundant assumptions, or examination of assumptions that noone previously bothered with taking as true

Math is convenient, but it is not necessary or intrinsic to observing the patterns or finding use in them. I know math and science are often found together, and I do not disagree anyone serious about science should study mathematics, but it is possible to utilize the scientific process without its study.

Wow that is amazingly naive. Mathematics is both necessary and intrinsic to the entire edifice of science and engineering and to the foundations of physics and has been since ancient times. This is not because somebody "made up" mathematics and "chose" it to provide tools for analyzing the physical world as physics. It was because it worked. It was not a choice of "convenience".

I went through the usual years of schooling enduring force-fed maths, all the while not appreciating its power or breathtaking

This is a metaphor which, while allowing us to grasp concepts, is subtly deceptive in itself. It happens that most people jump from metaphor to metaphor to understand the meaning of anything and glaring inconsistencies and errors creep in while one thinks or feels they understand.

I just want for someone to prove the Church-Turing conjecture for the set of all finite programs<->calclus. I specified finite as PM breaks down when dealing with an infinite number of elements into a set and Godel do not applies here as I do not search the truth value of a proposition, only a mapping D->P as I transform the parsing and interpretation of a finite description D to an hypothetical lambda calculus problem P. As long as all descriptions are finite and that the Church-Turing conjecture

There is a language of mathematics, but there is also something which is described by this language; so it is not correct to say that math is (just) a language. Also, if you try to describe certain phenomena without math, you just end up creating a math-like language to describe it I.e. certain things cannot be described without mathematics. Example: to describe the trajectory of a thrown baseball, you could say "it goes up and then comes down", which is fine but hardly precise; if you want more precision y

It should be illegal, because the harm it does to society beats all terrorists there can ever be.

You added that to get your post through the AC filter, didn't you? Your starkly worded post was veering into the territory of a sane and deeply held perspective on life. But it turns out you were man enough to rebalance the force, with your cross-category rampage. FYI you're deep into Chapter 8, "How Judgments Happen" from Thinking Fast and Slow.

Then what do you refer to the study of, and manipulation of logical systems including non-tradition (ie. meta-consistent logic). It is sometimes done by those who identify as philosophers, but I think you'll find that the majority of such work is done by people who identify as mathematicians and call it mathematics.
Math (according to anyone I know who has studied it deeply at least) is the thought process. The models and tools which are then applied to the real world are more often referred to as results

Yes that's all good mathematics but it may or may not have applications in physics. A mathematics built from an alternative logic system may not be of any use to a physicist since unless it works. But unusual mathematical structures have turned out to be useful in physics before.

I agree with your comment; although I don't see how what you said is relevant to what I said. GP was claiming that Maths was a product of logic (product of a way of reasoning), in response I claimed that logic was a subset of maths (ie. maths is a way of reasoning, one that encompasses the way of reasoing GP claimed maths was a product of).

Continuing with your line of discussion. There is some discussion of alternate logic in quantum physics. Usually largely in the realm of science philosophy/interpretation

Speaking of math, does anyone have a better link? The following kind of poked me in the eye:

But even if it is finite, researchersâ(TM) best guess is that it is no smaller than 10250 atoms of space and time. (Thatâ(TM)s the digit 1 followed by 250 zeros.) For comparison, the number of water molecules in all the oceans in the world has been estimated to be 4.4 x 1046

What? 10250 is not a one followed by 250 zeros, and there are a hell of a lot more than 4602.4 water molecules on Earth. Perhaps it's a

Maybe you just discovered that the "human way" of structuring science into theories is the same on an abstract level, if you look at all sections of natural science. Even the math related to a particular hard science is a Human Creation, after all. How do you know the people on, say, Alpha Centauri haven't developed a calculus which is radically different to ours and explains some physical effects much better than ours ?

On a very basic philosophical level we have to understand that all math is just modellin

I have learned that those that assume expertise in one area grants special insight into other areas often make fools of themselves.

I never mentioned special insight, just the regular kind. If you're a police officer for long, you learn something about psychology. Same with technical support. If you are an engineer, you'll find it easier to learn the legal system or medicine as well. While the fields have very different subject material, there are many underlying cognitive tools and processes that are similar. Using a screwdriver, hammer, wrench, etc., you can build a car, a house, a ship, or a skyscraper.

We are all connected. Our posts, Karma Whores and Trolls alike, give birth to Slashdot. Our insights and banal pontification ripple through time. From womb to tomb, some folks are addicted to spending all their waking hours brain farting here and the best you can hope for is to be up wind.

Maybe this is just because we use the same neural mechanisms we think with to phrase scientific theories and build models of networks? Just a thought.

If you look at enough phenomena, and generalize the description adequately, you'll find equivalences in a variety of strange places. The XKCD strip from friday is a good example. Also, If I see a picture of Jesus in my toast, can I get funding for a study? Seems to be the same "phenomena" at work.

Conflating the fact that human beings are given to seeing faces everywhere (its part of our primate survival hard wiring and allows mothers and infants to bond at birth), with seeing and appreciating the fractal and inherently consistent nature of the universe is at once myopic, and at the same time deeply ignorant. From the birth of the Renaissance geniuses like Leonardo DaVinci saw the recurring patterns of nature. Noticing how the number Phi shows up again and again in physical systems from the budlets in the heart of a daisy to the swirl of a galaxy is not self delusion but the human mind extracting meaning from the vast cacophony of the universe. The fact that your body is self similar on many scales, as is our planet and the very universe itself, and that these self similarities transcend scales of space and time is illuminating, is awe inspiring. You are indeed a product of this universe, you bear the mark of its rhythms and harmonies. You have 5 fold symmetry, because one of your oldest ancestors was related to a starfish (echinoderm) you don't find it the least bit fascinating that the shape of you brain models the shape of the universe itself and is in fact the universe attempting to understand itself. Are you so apathetic that the shear mystery and magnificence of life in this place doesn't occasionally move you tears of joy or dumbstruck wonder?

If so, than I am so sorry for you. You've been born into the greatest show ever and can't seem to take your eyes off your own feet. By the way, nice shoes.

How very poetic. Now let's be cold, mechanical and logical for a second and try to extract a falsification condition here.

On one side, we have the thesis that human brains are disposed to see particular patterns in the world. This is something that Cognitive Neuroscience investigates in considerable detail. We are gradually mapping out the structure of the brain, but are doing so through a process of experimentation and peer review, and with the aid of technology that we've developed to let us look in mo

Spot on. "[T]he measuring device has been constructed by the observer, and we have to remember that what we observe is not nature in itself but nature exposed to our method of questioning." Heisenberg, Werner (1958). Physics and Philosophy.

'By no means do we claim that the universe is a global brain or a computer,' said Dmitri Krioukov, co-author of the paper

Don't worry, 100,000 conservatives will draw an even better conclusion that you have proved that the Universe was intelligently designed, just like the brain.

Other scientists will of course point out that these structures are due to nothing more special than 'math'. Bill O'Reilly will feature one of the crazier ones on his program to show how stupid they are.

Just yesterday I read this 2007 review [ams.org] of Hofstadter's Strange Loop by Gardner, and it starts

Our brain is a small lump of organic molecules.It contains some hundred billion neurons, eachmore complex than a galaxy.

When I read this I thought, as much as I admire Martin Gardner, what a stupid thing to say. How can a galaxy, i.e. something that contains solar systems that contain at least one biosphere that contains billions of human brains, be less complex than a human brain. This assertion could only be true if you use some measure of complexity that discounts smaller dimensions, that regards complexity only on the outer layers of something. Now I see he might be wrong even on the galactic level.

It turns on the definition of complexity itself, which is not so straightforward as one might imagine [wikipedia.org]. One of the keys to many definitions of complexity lies not in the number of different parts, but in the non-trivial and adaptive ways those parts interact. Yes, there may be humans in this galaxy, but the relationships between those humans have no effect on the galaxy, qua galaxy. In other words, the interactions that occur on a galactic level produce no appreciable feedback in the system as a whole from human beings. Yet it is feedback and adaptation that occurs in complex systems that make them complex. As a complex system, therefore, the galaxy is not concerned with the presence of humans.

The same cannot be said of the relationship between neurons as a system and the brain as a system. As the article says, each neuron has its own level of complexity and this is in turn connected to the larger system of the brain, itself having billions of adaptive connections. Yet what is missing, but I think implied, is that the complexity within each neuron is non-trivial to the interactions between neurons.

Also, I wouldn't think less of a man who very occasionally indulges in hyperbolic excess. This does not make him stupid, only a lively writer.

In the event that humans were able to become technologically sophisticated enough to affect changes on a galactic scale - either through huge interactions or through tiny, replicating interactions with bigger consequences, then the galaxy as a complex system would be concerned with the existence of humans. If that ever has or shall occur, in whatever minute way, then the galaxy is necessarily concerned with the entire historical existence of humans, as affecting that interaction.

If one space probe we've sent out is even the merest flap of a butterfly's wing in the galaxy, then the galaxy as a complex system is concerned with humans. I'm pretty sure we've done more than that.

No, we haven't. Of the two Pioneers, one is just outside the solar system, light years away from any other system. And it's not a butterfly on Earth type thing, more like a microbe's effect on Earth's weather. You obviously have no idea how big a galaxy is.

Yes, there may be humans in this galaxy, but the relationships between those humans have no effect on the galaxy, qua galaxy. In other words, the interactions that occur on a galactic level produce no appreciable feedback in the system as a whole from human beings.

I'm going to have to look up the original paper published by Krioukov, but what was mentioned in the article itself is not news. I imagine this is a consequence of Krioukov trying to explain his findings in laymen's terms.

What the article actually says is a pretty basic exposition of the findings of network science [wikipedia.org] and complex systems theory [wikipedia.org] over the past few years. For those interested in but unfamiliar with these matters, I recommend a volume written a couple of years ago by the physicist Albert-László Barabási [wikipedia.org] called Linked: The New Science of Networks [barnesandnoble.com]. It is written for a wide audience and is a very readable introduction to the subject. Barabási's based argument is that these common network patterns we see in so many environments is a consequence both growth and preferential attachment in systems. Of course, growth and preferential attachment are going to be present in biological and social systems, as well as things like computer networks, and this is at the heart of why we see similar patterns forming (esp. scale-free topologies).

As a historian, I find the findings of network science as its been applied to social systems particularly useful. It helps to explain societal changes in ways that older theories of history, whether deriving from Marxian, Annaliste, Weberian, or other schools of thought, would have difficulty. Further, the study of networks and complex systems is inherently interdisciplinary--and this in a refreshingly honest way rather than the mere "interdisciplinarity" rhetoric that's been present in the academy over the years. For those interested in the application of network science to the social sciences, there is a very nice collection of seminal articles for the field edited by Gernot Grabher and Walter Powell [worldcat.org].

Jurgen (14843) below was kind enough to provide a link to the original paper below. There is actually some news here, but it's obscured by the news article linked. The news article discusses the common structure between brains, the internet, and the cosmos. This is not news for anyone familiar with complex systems. (And those who're unfamiliar with complex systems are easy to find here, because they're posting about this being bad science.)

This is just more Chopra-esque woo. The entire idea amounts to seeing images in clouds: our minds see patterns and similarities all over the place, even when there are none in reality.

No, the laws that govern the formation of structure in the universe really have nothing whatsoever to do with the laws that govern the formation of brains, let alone the Internet. These are three very different kinds of things with three very different mechanisms for building them, and which do very different things. The

Exactly. I suspect that when people see the word "network" used, they misunderstand its meaning. The brain and the universe are not like networks and we do not merely see network patterns in them. They are in fact networks because by the word network we mean a set of interlinking or interacting nodes. Under this definition, it does not matter what sort interactions may occur. The interactions can carry data (computer network), electricity (the grid), nutrition (the food cycle in biology), or mass (as we fin

The article is disappointingly vague and hand-wavy. Either the science is bullshit, or this summary is. Given that it's from India, I am leaning towards guessing the former; there's a lot of great research that happens in the country, but there's also a lot of pseudoscience that happens that's designed to give warm fuzzies to Indian nationalists who think they can undo the horrors of colonialisation and recapture national pride by beating the drum of "Vedic Math". Some of their flashier salesmen make it to the US and sell it to deluded new-agers and the other uneducated, portraying it as exotic deep knowledge "from the East".

I find it hard to believe that claims like this are supportable as good science at this point.

[...]said Dmitri Krioukov, co-author of the paper, published by the Cooperative Association for Internet Data Analysis (CAIDA), based at the San Diego Supercomputer Center (SDSC) at the University of California, San Diego.

Later:

[...]SDSC Director Michael Norman added [...]

And finally:

After the downscaling, the research team turned to Trestles, one of SDSC’s data-intensive supercomputers, to perform simulations of the universe’s growing causal network. By parallelizing and optimizing the application, Robert Sinkovits, a computational scientist with SDSC, was able to complete in just over one day a computation that was originally projected to require three to four years

Thanks to those scientists we now know that the Higher Power that created the universes is either using a templating system or has very strict design patterns, which means that if someone finds a flaw in internet the exploit could possibly be reused to hack the human brain or even destroy the universe. Let's hope the terrorists don't find out!

Turns out complex systems with a scale-free topology (the node density of which follows a power law rather than a gaussian function), of the kind we find in ecosystems, power-grids, computer networks, DNA, etc., all have similar strengths and vulnerabilities. Unlike random distributions, scale-free topologies are highly resistant to random failure: i.e. random deaths of animals of different sorts do not cause an ecosystem failure or random power stations failing does not necessarily cause a grid to collapse. This is what network and complex systems theorists call robustness. Scale-free topologies are, however, very vulnerable to directed attacks. Turns out certain creatures occupy more important spaces in ecosystems than others (they're hubs, with a high density of connections). Kill these off and an entire ecosystem can collapse. Likewise, hit certain power stations with high density of connections and you'll see cascading failures. A few random genes are damaged, chances are that a creature will survive and reproduce without problems. Screw around with the TP53 gene in humans, however, and expect some nasty results.

Finding similarities in abstractions is what humans do. If humans can describe something based on patterns that humans are capable of processing, then we will probably find them elsewhere! Abstraction doesn't give us mystical powers [wikipedia.org] that allow us to divine the "true nature [google.com]" of the universe (let alone understand what that questions means [wikipedia.org]).

Of course the network representing the structure of the universe is astronomically huge – in fact it can be infinite. But even if it is finite, researchers’ best guess is that it is no smaller than 10250 atoms of space and time.

The internet has not only made the world a smaller place, but the entire universe.

I prefer to think that the way the universe is is the way the universe is and that we just tend to see patterns in it because we are broken and need to change our perspective to that where the pattern is the default.

Changing maths to a base system on prime numbers doesn't work apparently. I don't know why.

Maybe the common thread behind the similarity is the method of reducing the problem so as to run efficiently on your favorite big iron.

I don't trust their portrayal of what they've discovered as far as I can spit. The details given are far below the threshold of critical thinking. Properly, a claim like this needs a triple helping of sharp knives.

For those of us who struggle with geometry, this is an explanation by CBS news...

The universe may grow like a giant brain, according to a new computer simulation. The results, published Nov. 16 in the journal Nature's Scientific Reports, suggest that some undiscovered, fundamental laws may govern the growth of systems large and small, from the electrical firing between brain cells and growth of social networks to the expansion of galaxies. "Natural growth dynamics are the same for different real networks

We already know that the planet Earth was created by hyper-intelligent pan-dimensional beings as part of a ten-million-year program running a computational matrix to compute the Ultimate Question of Life, the Universe, and Everything. Is it so far-fetched to believe the Universe itself is not the Internet of Life?

On the other hand, there is a theory which states that if ever anyone discovers exactly what the Universe is for and why it is here, it will instantly disappear and be replaced by something even m

If I was going to post such blather, I'd do it as an AC too. Math is a way of expressing how we perceive things. It has absolutely nothing to do with how things actually are. It is the ultimate anthropomorphization of reality.

Consider laws as a scribbling on a piece of paper that is stuffed in a paper bag. Laws do nothing.

Duh. The "laws" we formulate are simply our attempts to describe and predict what we can observe. When you throw a ball, the simplified model of gravity and the ball you have in your head doesn't affect reality in any way other than helping you predict where the ball goes.